Radio transmissions have been utilised for detecting objects for many years, since the first radar (radio detecting and ranging) systems. Radar is an example of an active sensing system, in which a radio signal is specifically transmitted towards a target or area of interest, and reflected signals are then analysed to detect any target within the area of interest. Active sensing systems such as radar are very widely used in many applications, such as air traffic control, meteorological measurements, and so on.
Another form of radio sensing is passive sensing, in which there is no specific transmission of a radio signal towards a target. Rather, passive sensing relies on existing (background) radio signals that are generated and utilised for other purposes, and detects reflections from these other signals in order to investigate a target. Passive sensing is attractive in circumstances in which is not feasible or desirable to use a specific radio transmission for active sensing. For example, in a military context, an adversary may detect a specific radio transmission being used for active sensing. This detection may warn the adversary that surveillance is being performed, and it may also allow the adversary to track back to the installation that is responsible for the specific radio transmission. However, in passive sensing, the adversary is unable to determine that surveillance is being performed, since only the background radio transmissions (and their reflections) are present.
One known method of performing passive sensing involves synchronously recording two separate signal streams. One stream is called the reference channel and is a direct measurement of a background radio signal being transmitted from a particular location. The other stream is called the surveillance channel and receives multiple copies of the transmitted (background) signal after potentially multiple reflections via any targets of interest, clutter and multipath. The surveillance channel may also receive the transmission (background) signal directly from the particular location—i.e. through a direct transmission from the origin of the signal, without any reflections, etc. This receipt of the directly transmitted signal represents an unwanted and problematic component, and is often referred to as direct signal interference (DSI).
In a typical implementation, the reference and surveillance channels are down-converted to either baseband or intermediate frequencies and digitized to produce signals which are represented as two large size complex 1-D arrays. The size (N) of the 1-D array depends on integration time T (s) and sampling rate R (samples/s) and is given by N=T·R. The reference and surveillance channel arrays can therefore be represented by:                Reference Channel: X=[x1, x2, . . . , xN]        Surveillance Channel: Y=[y1, y2, . . . , yN]where xi and yi are the complex array entries.        
Processing of the surveillance signal involves searching for at least one time-delayed, Doppler-shifted copy of the reference signal. This is achieved by calculating the cross-ambiguity surface G(j,n) between the surveillance and reference signals measured by the system according to equation (1) below.
                              G          ⁡                      (                          j              ,              n                        )                          =                              ∑                          k              =              0                                      K              -              1                                ⁢                                          ⁢                                    x              k                        ⁢                          y                              k                +                j                                      ⁢                          e                                                -                  2                                ⁢                π                ⁢                                                                  ⁢                i                ⁢                                  nk                  K                                                                                        (        1        )            The output from equation (1) is a 2-dimensional array commonly known as the cross-ambiguity surface. One dimension (n) in the array indicates the Doppler frequency shift of a signal reflection detected in the surveillance channel, which can be translated into a target velocity. The other dimension (j) represents the time-delay between the reference and surveillance channels and can be interpreted as a target range. The cross-ambiguity surface is therefore sometimes referred to as a range-Doppler surface.
Equation (1) is based on the ambiguity function, which is a two-dimensional function of time delay and Doppler frequency and is often used in radar to determine the distortion of a returned pulse due to the receiver matched filter (commonly, but not exclusively, used in pulse compression radar) due to the Doppler shift of the returned pulse from a moving target. The ambiguity function is determined by the properties of the pulse and the matched filter, rather than any particular target scenario. Many definitions of the ambiguity function exist (depending on the particular circumstances); for a given complex baseband pulse s(t), the narrowband ambiguity function is given by:x(τ,f)=∫−∞∞s(t)s*(t−τ)ei2πftdt  (1A)where * denotes the complex conjugate. Note that for zero Doppler shift (f=0) this reduces to the autocorrelation of s(t). The result after completing the ambiguity function of Equation (1A) is called the (cross)-ambiguity surface, and the generation of this (cross)-ambiguity surface is often referred to as ambiguity processing. It will be appreciated that Equation (1) is a discrete version of Equation (1A) (for use with sampled data), with the reference signal corresponding to the pulse s(t), and the surveillance signal corresponding to the reflected version of this signal.
As an example, if the surveillance signal contains a component corresponding to the reference signal, but with a time delay Δt with respect to the reference signal itself, this indicates that the component has traveled an additional distance of cΔt with respect to the reference signal (where c is the propagation speed of the radio signal). Similarly, if the component of the surveillance signal has a frequency shift of Δf with respect to the reference signal, this indicates that the target which produced the reflected signal is approaching towards or receding from the receiver (depending on the sign of the frequency shift) with a speed of ˜λΔf (where λ is the wavelength of the radio signal). N.B. the exact speed of approach or recession is dependent on the geometry between the original transmitter, the target, and the receiver (which will generally not be known). In addition, it will be appreciated that if Δf≠0, then Δt will change as the target moves towards or away from the receiver.
One difficulty with passive sensing is the need to search through the surveillance signal in both time and frequency (j and n respectively in equation 1 above) in order to locate any component(s) of the reference signal in the surveillance signal. This can make it rather challenging to perform passive sensing in a real-time, dynamic context.